Correlation and Regression

Question 1

Correlation

Answer 1

Correlation is the statistical relationship between variables such that change in one variable affects change in another variable

Question 2

Analysis of _______________ of two or more variables refer to __________________

Answer 2

Analysis of covariance of two or more variables refer to correlation

Question 3

Types of correlation

Answer 3

1.) Positive correlation
2.) Negative correlation
3.) Linear and non-linear
4.)Partial and total

Question 4

What does positive correlation indicate?

Answer 4

A positive correlation means that as one variable increases, the other also increases and as one decreases, the other decreases

Question 5

What does negative correlation indicate?

Answer 5

A negative correlation means that one variable increases, the other variable decreases and vice versa

Question 6

How to denote correlation coefficient

Answer 6

γ (gamma)

Question 7

What is correlation coefficient
(definition)

Answer 7

It is a numerical measure that quantifies the strength and direction of linear relationship between two variables

Question 8

Range of correlation coefficient

Answer 8

[-1,1]

Question 9

What does γ=0

Answer 9

At γ=0 indicates no linear relationship between two variables
or
covariance(x,y) = 0

Question 10

Example of real world positive correlation

Answer 10

Height and Weight

Question 11

Example of real world negative correlation

Answer 11

Supply and demand

Question 12

Value of γ for perfect positive correlation

Answer 12

1

Question 13

Value of γ for perfect negative correlation

Answer 13

-1

Question 14

Value of γ for partial positive correlation

Answer 14

0 < γ < 1

Question 15

Value of γ for partial negative correlation

Answer 15

-1 < γ < 0

Question 16

Value of γ for no correlation

Answer 16

0

Question 17

What is scatter plot used for

Answer 17

To visualize linear correlation between two variables

Question 18

Scatter diagram of perfect positive correlation

Answer 18

Question 19

Scatter diagram of perfect negative correlation

Answer 19

Question 20

Scatter diagram of partial positive correlation

Answer 20

Question 21

Scatter diagram of partial negative correlation

Answer 21

Question 22

Scatter diagram of no correlation

Answer 22

Question 23

Linear correlation

Answer 23

Changes in one variable are associated with proportional changes in the other, either positively or negatively.

Question 24

Non-linear correlation

Answer 24

Changes in one variable are not associated with proportional changes in the other

Question 25

Methods of studying correlation

Answer 25

1.) Graphic methods * a.)Scatter diagram * b.)Simple graphs 2.)Mathematical Methods * a.)Pearson's coefficient of correlation (γ) * b.)Spearman's rank coefficient of correlation (ρ)

Question 26

Coefficient of correlation

Answer 26

Pearson Coefficient of correlation

Question 27

Property second of coefficient of correlation

Answer 27

Question 28

Third property of coefficient of correlation

Answer 28

Question 29

Fourth property of coefficient of correlation

Answer 29

Question 30

Answer 30

Question 31

Answer 31

Question 32

Answer 32

Question 33

If X, Y are orthogonal in nature, what about its correlation

Answer 33

γ = 0 since orthogonal vectors are independent vectors

Question 34

Cov(X,Y)

Answer 34

E(XY) - E(X).E(Y)

Question 35

Definition of rank correlation coefficient

Answer 35

This method based on rank is useful in dealing with quanlitave characteristics such as morality, character, beauty. It is based on the ranks given to observations .

Question 36

Full name of rank correlation coeffiecient

Answer 36

Seaman's rank correlation coefficient

Question 37

How to denote rank correlation coefficient

Answer 37

ρ

Question 38

Formula of rank correlation coefficient

Answer 38

Question 39

Range of rank correlation coefficient

Answer 39

ρ ∈ [-1,1]

Question 40

Property second of rank correlation coefficient

Answer 40

If ρ =1, there is complete agreement in the order if the ranks and direction of ranks is same

Question 41

Property third of rank correlation coefficient

Answer 41

If ρ =-1, there is complete disagreement in the order of ranks and they are in opposite directions

Question 42

if ρ=1, then

Answer 42

If ρ =1, there is complete agreement in the order if the ranks and direction of ranks is same

Question 43

If ρ =-1, then

Answer 43

If ρ =-1, there is complete disagreement in the order of ranks and they are in opposite directions

Question 44

Regression

Answer 44

Approximate relationship between two random variables X and Y is called regression. The method is to estimate the unknown value of one variable from the known value of other variable is called regression.

Question 45

Type of regression

Answer 45

Linear Non-linear regression

Question 46

Line of regression (definition and another name)

Answer 46

The line described in the average relationship between two variables is known as line of regression or estimating line.

Question 47

What can we calculate using regression coeffiecient

Answer 47

We can calculate the coefficient of correlation using regression coefficient.

Question 48

Explain error and also related to it (Linear regression of X and Y)

Answer 48

Question 49

Statistical interpretation (regression line) (2)

Answer 49

Question 50

Regression line equation of X on Y is

Answer 50

Question 51

Regression line equation of Y on X is

Answer 51

Question 52

Regression coefficient X on Y is

Answer 52

Question 53

Regression Coefficient Y on X is

Answer 53

Question 54

Correlation coefficient in terms of regression coefficients

Answer 54

Correlation coefficient is geometric mean of regression coefficients

Question 55

Relationship between regression coefficient and regression coefficients

Answer 55

We know that Arithmetic mean > geometric mean

Question 56

Probable error

Answer 56

Question 57

Standard Error of coefficient of correlation

Answer 57

Question 58

Point of intersection of regression lines

Answer 58

Question 59

If there is two regression lines, how do you decide which one is of y on x and which one is of x on y

Answer 59

Question 60

Important note of regression lines

Answer 60

If two regression lines of y on x and x on y are respectively a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 then a₁b₂ < a₂b₁

Question 61

Angle between two regression lines

Answer 61

Question 62

Two special points about angle of regression and correlation coefficient

Answer 62

If γ=0 then θ=π/2 If γ=±1 then θ=0 or π

Question 63

Sign about coefficient of regression and correlation coefficient

Answer 63

Question 64

Regression line y on x passes through

Answer 64

(mean of x, mean of y)

Question 65

Regression line x on y passes through

Answer 65

(mean of x, mean of y)